Hermann Minkowski (1864-1909)

Hermann Minknowski was born in Kaunas (Lithuania), and studied in Königsberg, Germany. After World War II, this city became the Russian city of Kaliningrad. This city was the geographical environment for Immanuel Kant to produce his philosophy, which served as the philosophical base for Einstein. You may click on the following links for While Königsberg was a port city like Venice, Kaunas was in its hinterland. Here are two maps telling where they are.

The University of Königsberg (Albertina University) had many mathematicians interested in physics. They were particularly interested in Maxwell's equations. We are now using the form of Maxwell's equations developed there. Minkowski continued his research in those equations after he left Königsberg.

He was a professor of mathematics and physics at the University of Zurich, while Einstein was a student there. There he completed the proof that Maxwell's equations are covariant under Lorentz transformations. He published his result in 1908.

Is this the end of the story of the Lorentz covariance of Maxwell's equations? No. This problem was not completely settled until 1990. We shall talk about this next time.

Another important contribution Minkowski made is the Minkowski space where

is a Lorentz-invariant quantity. If we do not change the x and y variables,

We are quite familiar with the two-dimensional geometry associated with hyperbolic condition. But this geometry is still is strange to us. I am not the first one to feel in this way. It was Paul A. M. Dirac who invented the light-cone coordinate system to deal with this problem. However, the problem with Dirac was that he never draws pictures in his papers, unlike John A. Wheeler.

Let us write the above formula as

If we introduce the "light-cone" variables

the Minkowskian geometry becomes the geometry of rectangles, with u and v for two perpendicular sides. If the area of the rectangle remains constant, one side becomes contracted when the other side expands. This is the geometry of squeeze.

I learned this geometry during my high-school years. Since 1973, most of my papers are based on this squeeze geometry. This geometry is not only useful for Lorentz-boosted particles, but also provides the basic mathematical language for optical sciences.

Recent Photos from Lithuania

I went in September (2008) to Vilnius to attend the 12th International Conferece on Quantum Optics and Quantum Information. As usual, I brought my camera with me and took a number of photos. I would like share some of them with you.

Y. S. Kim (2008.10.10)

copyright@2008 by Y. S. Kim, unless otherwise specified. The portrait of Hermann Minkowski is from http://library.thinkquest.org/05aug/01273/whoswho.html.